论文标题
在单调均值变化的偏好下，CRAM {é} R-Lundberg风险模型的最佳投资和再保险政策
Optimal investment and reinsurance policies for the Cram{é}r-Lundberg risk model under monotone mean-variance preference
论文作者
论文摘要
在本文中，在保险公司的角度考虑了单调均值变化（MMV）标准的优化问题。 MMV标准是经典均值（MV）标准的修订版，可确保实用程序函数的单调性。通过此标准，我们研究了最佳的投资和再保险问题，该问题被称为保险公司和虚构玩家之间的零和游戏。我们应用动态编程原理来获得相应的汉密尔顿 - 雅各比 - 贝尔曼 - 伊萨克斯（HJBI）方程。作为本文的主要结论，通过明确求解HJBI方程，获得了最佳策略的封闭形式和价值函数。此外，还提供了MMV有效的边界。在论文的最后，提出了一个数字示例。
In this paper, an optimization problem for the monotone mean-variance(MMV) criterion is considered in the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance(MV) criterion which guarantees the monotonicity of the utility function. With this criterion we study the optimal investment and reinsurance problem which is formulated as a zero-sum game between the insurance company and an imaginary player. We apply the dynamic programming principle to obtain the corresponding Hamilton-Jacobi-Bellman-Isaacs(HJBI) equation. As the main conclusion of this paper, by solving the HJBI equation explicitly, the closed forms of the optimal strategy and the value function are obtained. Moreover, the MMV efficient frontier is also provided. At the end of the paper, a numerical example is presented.
